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Question 1039370: I need help working through this problem. Mostly just B with Descartes law of signs.
a) Use the RZT Theorem to show the possible rational roots.
b) Use Descartes law of signs to deduce the possible # of positive and negative roots.
c) Use synthetic division, polynomial division, or the Remainder Thm to find all the real roots
1. 2𝑥^3 + 3𝑥^2 − 8𝑥 + 3
a. _____________________
b. POS #________________
b. NEG #________________
c. _
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I need help working through this problem. Mostly just B with Descartes law of signs.
1. f(x) = 2𝑥^3 + 3𝑥^2 − 8𝑥 + 3
f(-x) = -2x^3 + 3x^2 + 8x + 3
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a) Use the RZT Theorem to show the possible rational roots.
Factors of 3:: +-1 ; +-3
Factors of 2:: +-1 ; +-2
Ans: +-1 ; +-1/2 ; +-3 ; +-3/2
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b) Use Descartes law of signs to deduce the possible # of positive and negative roots.
# of positive <= # of sign changes of f(x) = 2
# of negative <= # of sign changes of f(-x) = 1
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c) Use synthetic division, polynomial division, or the Remainder Thm to find all the real roots
1)....2....3....-8....3
......2....5....-3...|..0
Solve 2x^2 + 5x -3 = 0
(2x-1)(x+3) = 0
Ans: x = 1 or x = 1/2 or x = -3
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Cheers,
Stan H.
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